# Selecting Suitable MODFLOW Packages to Model Pond–Groundwater Relations Using a Regional Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}, while the underlying Almonte-Marismas aquifer system has an area of 2640 km

^{2}(Figure 1a). This coast pond is linked to the evolution of the dune buildings located in a large deflation basin of the ancient dune systems. Locally, there is no information on the variability of the parameters of the aquifer and the pond bed. Almonte-Marismas aquifer comprises a free detrital aquifer, where the permeable materials are under the sands and marsh, and semi-confined where they were under the thick detrital materials or confined under materials of low hydraulic conductivity (such as marshland clays) [35]. Groundwater flows from the aquifer to the Santa Olalla pond and, generally, moves from the northeast to the southwest (Figure 1b,c). Nevertheless, it has been verified that, during some extremely dry seasons, Santa Olalla pond changed its direction of flow and started to discharge from the pond to the aquifer along the southern side of the shore [26,33,36]. Doñana has a sub-humid Mediterranean climate with Atlantic influence, it is characterized by regular temperatures, short mild winters, in which temperatures below 0 °C are rarely reached, and dry summers with more extreme temperatures (sometimes exceeding 45 °C). Rainfall is quite variable, and it is characterized by the hyper-annual and interannual variability of rainfall (yearly average 575 mm).

#### 2.2. Data

^{−3}m/d, and the annual average free water evaporation was (EV) 4.56 × 10

^{−3}m/d. The flow from the aquifer to the pond was calculated using the mass balance equation:

_{observed}= (P − EV) × A,

^{3}/year, and this value was then used to evaluate the model performance at the local scale. This value is a bit higher than the estimation obtained by Lozano [33], who calculated it to be approximately 0.2 hm

^{3}/year, by applying a local mathematical model. A much greater value was estimated in [34], with a 2D segmented-Darcy approach. These authors calculated 1.32 hm

^{3}/year of groundwater discharge to the Santa Olalla pond over a seven-month period (between the summer and autumn of 2016). The simplicity of the 2D numerical model, the period of study during the dry season and the underestimation of the aquifer depth (from 2 to 10 m upper layer thickness) could be the reasons for the high aquifer discharge value.

^{2}+ (Observed lake stage − Simulated lake stage)

^{2}+ (Observed outflow – Simulated outflow)

^{2}

#### 2.3. Reference Regional Groundwater Model

#### 2.4. MODFLOW-LGR

#### 2.5. MODFLOW Boundary Conditions Representing the Pond

_{D}, is a parameter imposed by the coefficient of proportionality. The quantification for this flux exchange is expressed by the following equation [22]:

_{D}= C

_{D}× (H

_{D}− h),

_{D}is the discharge from the aquifer through the pond (L

^{3}/T), C

_{D}is the conductance of the pond bed (L

^{2}/T), H

_{D}is the stage of the DRAIN (L) and h is the aquifer head at the pond location (L).

_{D}(see Equation (3) and Figure 3a), can be proportionally computed to the ratio between the area of the polygon, limiting the boundaries of the drain and the area of cell, Ac (Figure 3b). If this option is chosen (i.e., the conductance interpretation is set to be calculated), then the ModelMuse input parameter is considered as conductance per unit area, C

_{D}/A

_{c}(1/T), and the total conductance is equal to this parameter multiplied by the area of the polygon delimitating the drain boundary condition. The parent and child models have different cell sizes and, hence, total conductance in each cell is not the same in both models.

^{−3}m/d was employed, decreasing this value linearly from the surface to 0.5 m depth. The EVT extension and location were estimated from the difference between the maximum and average flooded Santa Olalla area (Figure 3b).

_{RBed}in Figure 4) and the head in the river (H

_{R}in Figure 4) are necessary parameters. Interchange flux direction depends on the head in the cell connected to the river. If this head drops below the bottom of the riverbed, water enters into the aquifer at a constant rate defined by the gradient between the level of the river and the elevation of the pond bed. When it is above the bottom of the river, water will either leave or enter the aquifer depending on whether the head is above or below the head in the river. The quantification for the flux exchange with this boundary condition is the same as Equation (3), multiplying a conductance term by the difference between the head in the cell and the head in the river. The conductance of the river is defined by Equation (4):

_{R}= (K

_{R}× L × W)/M,

_{R}is the hydraulic conductivity of the riverbed material (L/T), L is the length of reach (L), W is the width of the river (L) and M is the thickness of the riverbed (L).

_{R}) was set to the average water level measured in the pond (5.25 m a.s.l.). Five different objects were used to represent the river bottom of the pond (Figure 4b) by using bathymetry data taken from [43], ranging from 0.2 to 2.5 m under the ground surface, in the child cells. In the case of the parent river cells, this boundary condition involves 4 cells of the regional model (Figure 4b).

_{b}, and the conductance of the aquifer, C

_{a}. These parameters define the equivalent conductance, C

_{e}(Figure 5) [14]:

_{b}= K

_{b}× A/b = L

_{b}× A,

_{a}= K

_{a}× A/Δl,

_{e}= (1/C

_{b}) + (1/C

_{a}),

_{e}= A/((b/K

_{b}) + (Δl/K

_{a})),

^{2}), K

_{b}is the hydraulic conductivity of lakebed material (L/T), K

_{a}is the hydraulic conductivity of aquifer material under the lake in direction Δl (either horizontal or vertical) (L/T), b is the lakebed thickness (L), ∆l is the thickness of the aquifer section (L), which corresponds to half the thickness of the cell below and beside the pond cell, and L

_{b}is the lakebed leakance (1/T). Though this formulation allows to differentiate between vertical and horizonal hydraulic conductivity of the regional aquifer, in the present case, layer 1 is isotropic and K

_{a}has the value in both directions. K

_{b}was also considered to be isotropic.

_{D}/A and C

_{R}/A) and lakebed leakance, L

_{b}, were adjusted with the trial and error approach. The performance aimed to reproduce the observed piezometric heads, the outflow to the pond and the pond stage in the case of using the LAKE boundary condition. Residuals are defined as the difference between observed and calculated values. The fit criterion was the minimization of the objective function results (Equation (2)).

## 3. Results and Discussion

#### 3.1. Reference Model Parent

#### 3.2. Parent vs. Child for DRAIN Package

_{D}/A, was carried out. The parent model residuals are shown in Figure 7a, while the child models results are displayed for both the vertical discretization with 4 layers (Figure 7b) and with 8 layers (Figure 7c).

_{D}/A increases, the absolute values of residuals decrease until zero, and after the residual continues increasing. This is explained by the fact that, when the conductance increases, the aquifer drains more water to the pond, which makes the calculated piezometric heads around the pond decline. Piezometric head residuals have a similar order of magnitude for parent and child models, being, on average, a little smaller in the child models for all piezometers. In other words, child discretization reproduces the observed piezometric heads slightly better than the parent model. For example, the residual average at the different piezometric heads is 0.61 m in the parent model and 0.54 m for the 4- and 8-layer models. Differences between the residual heads of the 4- and 8-layer models are very small (of the order of 10

^{−3}m). The vertical discretization of 8 layers (Figure 7c) presents a slightly higher mean residual piezometric head in PSO1 and PSO2A than with the 4-layer discretization (Figure 7b). However, PSOS and PSOW piezometers present smaller residuals in the 8-layer model than in the 4-layer one. The explanation of this feature is attributed to the bigger dispersion of residual piezometric heads within a vertical and horizontal refinement. This can be attributed to the greater horizontal and vertical discretization, where the model can describe the evolution of the piezometric heads in greater detail. That is why the child residuals improve with respect to the parent, and also, where the flow has an important vertical component (proximity of the pond, PSOS and PSOW), increasing the vertical discretization (from 8 to 4) also slightly improves the residuals. When the flow has a preponderant horizontal component, a greater vertical discretization may not contribute and ends up being counter-productive, as in PSO1 and PSO2A.

_{D}/A, is illustrated in Figure 8a (parent model), Figure 8b (4-layer child model) and Figure 8c (8-layer child model). As in the case of the piezometric residuals, the range of the residual outflow values do not show relevant differences between parent (0.54 hm

^{3}/year) (Figure 8a) and child models (0.44 hm

^{3}/year for both the 4- and 8-layer models) (Figure 8b,c). As was expected, when the conductance increased, the flux to the pond was higher. Water balance is influenced by the C

_{D}/A, and as C

_{D}/A increases, the values of the residuals decrease until a C

_{D}/A value is reached, between 2.5 × 10

^{−3}and 1 × 10

^{−2}1/d, where residuals are 0. For higher values of C

_{D}/A, the values of the residuals begin to increase (Figure 8).

#### 3.3. Parent vs. Child for RIVER Package

_{R}/A increases, the absolute residual values decrease until an optimum value of C

_{R}/A is reached, which makes the residuals close to zero. Then, for higher values of conductance, the simulated piezometric heads are lower than the observed values and absolute residual values begin to increase again (Figure 9).

_{R}/A being greater than 2.5 × 10

^{−3}1/d. The optimum C

_{R}/A value for the parent would be 2.5 × 10

^{−3}1/d with an objective function value of 0.17 and 2.5 × 10

^{−3}or 1 × 10

^{−2}1/d in the child models, with an objective function value of 0.18. On the other hand, outflow values do not seem to be unrealistic, and unlimited water input from the river boundary condition cells to the aquifer has been observed by other authors, such as Jones et al. [21].

#### 3.4. Parent vs. Child for LAKE Package

#### 3.4.1. Piezometry Results in the Parent Model (LAKE Package)

^{−3}1/d.

#### 3.4.2. Piezometry Results in the Child Models (LAKE Package)

_{b}) higher than 1 × 10

^{−2}1/d in both child models (in Figure 11 and Figure 12, colored grey). This fact could not be explained, and it was attributed to numerical instability problems, being smoother in the 8-layer model (Figure 11d vs. Figure 11f and Figure 12c vs. Figure 12d).

^{−3}and 1.25 × 10

^{−3}1/d (shown with dashed lines in Figure 11a,c,e). Residual piezometric heads are lower in the child models than in the parent model (order of 2 × 10

^{−1}m). For example, a leakance of 1 × 10

^{−2}1/d results in parent model residuals of 0.34 m (PSOS) or 0.49 m (PSO1) while, for the 8-layer child model, residuals are 0.17 m (PSOS) or 0.28 m (PSO1). On the other hand, piezometric head residuals are more sensitive to leakance values than in the parent model. The trend of the piezometric heads is similar in both the 4- and 8-layer child models. For these child models, a greater sensitivity to leakance was observed in the PSOS and PSOW piezometers. This could be due to their proximity to the pond.

_{a}, plays a major role in the equivalent conductance (Equation (6)). This happens because ∆l values are high in the discretizations used and, as the discretization is refined, K

_{a}loses weight in the equivalent conductance, Ce (Equation (8)). Due to this fact, it is important to note the importance of also simulating and evaluating the lake stage to get a realistic leakance value. Similarly, Jones et al. [21] noticed that horizontal hydraulic conductivity values for the aquifer have a large impact on the model’s ability to simulate lake water levels and base flows.

^{−4}1/d, the residuals of lake stage achieved 22.74 (Figure 11a), 14.99 or 8.04 m (Figure 11b). The solution is to align cell bottoms with the pond bathymetry. However, this approach is not always recommended due to the abrupt variations of discretization that could be produced. This fact was somehow pointed out by Jones et al. [21] when they stated that the model that uses the LAKE package should be applied to simulations of hydrologic features and processes that can be accurately represented in the model area at the scale of the model cells. In any case, the literature consulted regarding the LAKE MODFLOW package does not explicitly prevent this problem. It is in the printed output file where it can be seen that the resulting lake stage has no physical meaning.

#### 3.4.3. Outflow Results (LAKE Package)

^{−3}1/d, and then, the residuals begin to increase. In the parent model, outflow residuals do not get values close to zero for any studied leakance value. Both facts, again, are possibly happening because the water balance is preponderantly affected by the hydraulic conductivity of the regional aquifer K

_{a}, and the ‘great’ value of ∆l. In all the models, the outflow residual trend decreases as leakance gets higher (Figure 12) because as the leakance is greater, the discharge to the pond increases. Child models are more sensitive to leakance than the parent model, giving better possibilities for performance for the outflow residuals than using the parent model (Figure 12). The explanation is related to the higher ∆l values in the parent model, which reduce the influence of K

_{b}for the equivalent conductance, Ce (Equation (8)). Optimal leakance values are higher in the model with a discretization of 8 layers (from 1.19 × 10

^{−3}to 1 × 10

^{−2}1/d) than for 4 layers (from 2.9 × 10

^{−4}to 2.5 × 10

^{−3}1/d), and the residuals are lower for 8 layers than for the model with 4 layers.

^{−2}1/d (parent), 1 × 10

^{−2}1/d (4 layers) and 1.8 × 10

^{−2}1/d (8 layers), with the lowest objective function.

#### 3.5. Practical Aspects Using ModelMuse

_{D}, can be computed proportionally to the area of the polygon, limiting the boundaries of the drain (Figure 3b). If this option is chosen, then the ModelMuse input parameter is considered to be conductance per unit area, C

_{D}/A (1/T), and the total conductance is equal to this parameter multiplied by the area of the polygon delimiting the drain boundary condition, allowing a conductance calculation in each cell based on the intersected area between the object and the cell.

## 4. Conclusions

_{R}is imposed from the observed lake (or pond) stages. However, as H

_{R}is an input, this package should be rejected if measured pond water levels are needed as a calibration criterion. This package can be applied for gaining or losing surficial water bodies.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**,

**b**) Geological map of Doñana aquifer and location of Santa Olalla pond. (

**b**) Location of piezometers (PSO1, PSO2A, PSO2B, PSOW, PSOS, see Table 1) surrounding Santa Olalla pond and pond stage logger (SOL). (

**c**) Conceptual model.

**Figure 2.**(

**a**) Parent model horizontal view, (

**b**) parent model cross-section profile corresponding to the blue line (x-x’) in (

**a**), (

**c**) child model horizontal discretization of red area appearing in (

**a**), (

**d**) child vertical discretization into 4 layers for the blue profile shown in (

**c**) (y-y’), (

**e**) child vertical discretization into 8 layers for the blue line displayed in (

**c**) (y-y’).

**Figure 3.**(

**a**) Conceptual scheme of DRAIN package and (

**b**) cells where piezometers, drain and evapotranspiration boundary conditions were located in the parent and child models.

**Figure 4.**(

**a**) RIVER package scheme, (

**b**) child and parent model cells where the river boundary condition was introduced.

**Figure 5.**(

**a**) LAKE package scheme (modified from Merritt and Konikow [14]), (

**b**) cells where lake boundary condition was introduced in the child and parent models.

**Figure 6.**(

**a**) Regional calibrated hydraulic conductivity in the first layer of the regional model. Santa Olalla pond area, (

**b**) hydraulic conductivity in the whole aquifer and (

**c**) front view of hydraulic conductivity in the aquifer.

**Figure 7.**Performance evaluation analysis of piezometric heads to DRAIN conductance per unit area, C

_{D}/A, for (

**a**) parent model, (

**b**) child model with 4 layers and (

**c**) child model with 8 layers. * Piezometric heads (dashed lines) referred to reference values of the regional model.

**Figure 8.**Performance evaluation analysis of outflow from the aquifer to drain conductance per unit area, C

_{D}/A, for (

**a**) parent model, (

**b**) child model with 4 layers and (

**c**) child model with 8 layers.

**Figure 9.**Performance evaluation analysis of residual piezometric heads of (

**a**) parent model, (

**b**) child model with 4 layers and (

**c**) child model with 8 layers, with the boundary condition of RIVER. * Piezometric heads (dashed lines) referred to reference values of the regional model.

**Figure 10.**Performance evaluation analysis of residual outflow values of (

**a**) parent model versus (

**b**) child model with 4 and (

**c**) child model with 8 layers with the boundary condition of RIVER.

**Figure 11.**Performance evaluation analysis of residual piezometric heads of (

**a**) parent model, (

**b**) zoom of the parent model, (

**c**) child model with 4 layers, (

**d**) zoom of child model with 4 layers, (

**e**) child model with 8 layers and (

**f**) zoom of child model with 8 layers with the boundary condition of LAKE. Blue vertical dashed lines show specific calibrated leakance ranges. Between these two values, the model computed realistic lake stages, ranging from the lakebed and the maximum observed stage. The values of these realistic lake stages are indicated at the top of the dashed lines. The grey colored area shows abnormal results. * Piezometric heads (dashed lines) referred to reference values of the regional model.

**Figure 12.**Performance evaluation analysis of residual outflow values of (

**a**) parent model, (

**b**) zoom of parent model, (

**c**) child model with 4 layers and (

**d**) child model with 8 layers with the boundary condition of LAKE. Dashed lines show specific calibrated leakance ranges. Between these two values, the model computed realistic lake stages, ranging from the lakebed and the maximum observed stage. The values of these realistic lake stages are indicated at the top of the dashed lines. The grey colored area shows abnormal results.

Source | Name | X UTM | Y UTM | Average Observed Heads (m) | Max/Min Observed Heads (m) | No. of Measurements | Well Screen Depth (m) | Sensor (Brand) |
---|---|---|---|---|---|---|---|---|

(ED50 H30) | (ED50 H30) | |||||||

IGME | PSO1 | 190,112 | 4,098,731 | 6.33 | 6.78/5.84 | 1868 | 69.5 | OTT |

MiniOrpheus | ||||||||

IGME | PSO2A | 190,113 | 4,098,733 | 6.14 | 6.60/5.54 | 2230 | 27.5 | OTT |

MiniOrpheus | ||||||||

IGME | PSO2B | 190,113 | 4,098,733 | 6.44 | 6.59/5.75 | 1217 | 45 | OTT |

Orpheus | ||||||||

POU | PSOW | 190,142 | 4,098,479 | 6.08 | 6.48/5.46 | 2920 | 15.6 | MiniDiver |

POU | PSOS | 190,374 | 4,098,113 | 5.45 | 5.90/4.95 | 2920 | 2.5 | MiniDiver |

CD/A (1/d) | Obj. Function | Drain | Lake | River |
---|---|---|---|---|

0.0001 | Parent | 0.32 | 517.74 | 0.76 |

4 Layer | 0.42 | 225.17 | 0.73 | |

8 Layer | 0.42 | 64.93 | 0.73 | |

0.00015 | Parent | 0.31 | 229.43 | 0.73 |

4 Layer | 0.4 | 198.21 | 0.71 | |

8 Layer | 0.4 | 59.65 | 0.71 | |

0.00029 | Parent | 0.28 | 61.02 | 0.67 |

4 Layer | 0.37 | 88.83 | 0.65 | |

8 Layer | 0.37 | 45.64 | 0.65 | |

0.00119 | Parent | 0.16 | 3.77 | 0.38 |

4 Layer | 0.21 | 4.87 | 0.37 | |

8 Layer | 0.21 | 5.92 | 0.37 | |

0.0025 | Parent | 0.11 | 1.11 | 0.17 |

4 Layer | 0.12 | 1.22 | 0.18 | |

8 Layer | 0.12 | 1.44 | 0.18 | |

0.01 | Parent | 0.48 | 0.45 | 0.29 |

4 Layer | 0.28 | 0.4 | 0.18 | |

8 Layer | 0.27 | 0.47 | 0.18 | |

0.018 | Parent | 0.87 | 0.45 | 0.65 |

4 Layer | 0.5 | 3.56 | 0.37 | |

8 Layer | 0.48 | 0.34 | 0.36 | |

0.027 | Parent | 1.18 | 0.45 | 0.95 |

4 Layer | 0.65 | 4.12 | 0.52 | |

8 Layer | 0.63 | 0.56 | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Serrano-Hidalgo, C.; Guardiola-Albert, C.; Heredia, J.; Elorza Tenreiro, F.J.; Naranjo-Fernández, N. Selecting Suitable MODFLOW Packages to Model Pond–Groundwater Relations Using a Regional Model. *Water* **2021**, *13*, 1111.
https://doi.org/10.3390/w13081111

**AMA Style**

Serrano-Hidalgo C, Guardiola-Albert C, Heredia J, Elorza Tenreiro FJ, Naranjo-Fernández N. Selecting Suitable MODFLOW Packages to Model Pond–Groundwater Relations Using a Regional Model. *Water*. 2021; 13(8):1111.
https://doi.org/10.3390/w13081111

**Chicago/Turabian Style**

Serrano-Hidalgo, Carmen, Carolina Guardiola-Albert, Javier Heredia, Francisco Javier Elorza Tenreiro, and Nuria Naranjo-Fernández. 2021. "Selecting Suitable MODFLOW Packages to Model Pond–Groundwater Relations Using a Regional Model" *Water* 13, no. 8: 1111.
https://doi.org/10.3390/w13081111